Finite p-groups of class 2 have noninner automorphisms of order p
classification
🧮 math.GR
keywords
classfinitenoninnerorderautomorphismautomorphismseitherelementwise
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We prove that for any prime number $p$, every finite non-abelian $p$-group $G$ of class 2 has a noninner automorphism of order $p$ leaving either the Frattini subgroup $\Phi(G)$ or $\Omega_1(Z(G))$ elementwise fixed.
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